Apple IDs cannot be merged. What exactly is going on so I can try and help you with the best possible solution?
Please remember I cannot see your devices so where is it popping up with those emails and what are you doing exactly?
It sounds like you have two Apple ID accounts on your devices which is confusing the issue with different email addresses popping up.
Take a look here: https://support.apple.com/en-us/HT203983
Follow those steps on each device and it should clear any issue with multiple email addresses; it will have you signed into only one account.
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